Former US presidential candidate John McCain is among a number of senior American politicians urging David Cameron to bar from Britain dozens of Russian officials implicated in the controversial death of a whistleblower.

The prime minister arrives in Moscow on Monday, his first visit to the Kremlin, amid mounting international pressure to follow the lead of the US by introducing visa bans for individuals linked to the death of lawyer Sergei Magnitsky.

The 37-year-old was working for a British company when he exposed the biggest tax fraud in Russian history. After accusing Interior Ministry officials, Magnitsky was arrested and died in police custody after being denied essential medical care. Investigators say the father of two was tortured and badly beaten in the hours before his death in November 2009.

The case has become a focal point for activists seeking to highlight state corruption in Russia. Cameron is being urged to make it clear that employees of British companies in Russia cannot be abused with impunity.

In July the case prompted the US secretary of state, Hillary Clinton, to introduce a travel ban and freeze the assets of 60 Russian officials implicated in Magnitsky's death. But even though Magnitsky was directly employed by William Browder, who runs a London-based investment fund, Hermitage Capital Management, the UK government has failed to act or even criticise the Russian authorities over the affair. On the eve of Cameron's trip, senior US officials said he needed to demonstrate his human rights credentials.

McCain, a US senator, told the Observer: "We hope the British government will seriously consider visa bans and asset freezes on the Russian government officials implicated in the torture and murder of Sergei Magnitsky, as we have proposed in Congress."

Democrat senator Benjamin Cardin, who tabled the Sergei Magnitsky rule of law and accountability bill, backed by 18 other senators, added: "I encourage the British and other governments to join the United States in imposing sanctions against the people who were involved in the death of Magnitsky. It is when allies work together on human rights that we can be most effective."

Pressure is also building on Cameron closer to home. Labour MP Chris Bryant, a former Foreign Office minister, said: "Britain should be making it absolutely clear that anybody involved in the corruption that Magnitsky revealed, or in his murder, is quite simply not welcome in this country. I hope Cameron is not going to be as gullible to swallow bland assurances by [president) Dmitry Medvedev and [prime minister] Vladimir Putin or be so eager to please that he fails to raise the important human rights abuses in relation to Magnitsky and [Mikhail] Khodorkovsky."

Khodorkovsky, the former chief executive of the oil company Yukos, was found guilty last year of theft and money laundering by a Moscow court, but is deemed a prisoner of conscience by Amnesty International.

Cameron's meeting with Putin will be the first official Russian contact with Britain since an unproductive bilateral meeting with Tony Blair during a G8 summit in 2007. Anglo-Russian relations remain tarnished by the murder of British citizen and Putin critic Alexander Litvinenko in London in 2006 with a radioactive isotope. Britain has repeatedly asked without success for the extradition of the chief suspect in the Litvinenko case, former KGB officer Andrei Lugovoi, who has since been elected to the Russian parliament.

Another former Foreign Office minister, Denis MacShane MP, believes Cameron should concentrate on bringing those responsible for Magnitsky's death to justice. "After grandiose claims about promoting human rights in Libya, David Cameron should not wimp out of supporting human rights in Russia, especially when it concerns a British citizen, a London-based firm and his murdered lawyer. It would be deplorable if the US and other EU states took the lead while Cameron refused to take similar action."

Browder said: "The prime minister has a very simple decision to make. Does he want the Russian officials who sadistically tortured and murdered a lawyer working for a British firm to be allowed to enter our country and use our banks? This is not a question that the government can avoid by hiding behind bureaucratic language. How the government answers this question will send a strong message to dictators around the world."

Downing Street declined to say whether Cameron would raise the case with Putin.